Incompatibility of New Symmetry Reductions in U(1) × U(2) × U(3) Gauge Group with Higgs Mechanism

Abstract

Noncommutative (NC) space-time leads to some strong constraints on the possible choices of gauge groups and allowed representations of matter and gauge fields. The standard model based on U(3) × U(2) × U(1) can be transcribed to NC space-time consistently with these constraints (Chaichian et al., Eur. Phys. J. C29:413, 1). In fact, through two new symmetry reduction mechanisms, this gauge group is reduced to the usual standard model one. In this paper, we show that, on the contrary to the usual standard model, the Goldestone boson equivalence theorem is violated due to the incompatibility of the new symmetry reduction mechanisms with the electroweak Higgs mechanism.